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Parameter estimation for fractional-order chaotic systems is a multi-dimensional optimization problem, which is one of the important issues in fractional-order chaotic control and synchronization. With the characteristic of quantum parallel, a new quantum parallel particle swarm optimization algorithm is proposed for solving the problem of parameter estimation in fractional-order chaotic systems. A new method of quantum coding is presented with quantum parallel characteristic which can make the calculation number of each generation increase exponentially. On the basis of this method, a particle evolution equation composed of quantum current rotation angle, individual optimal rotation angle, and global optimum rotation angle is proposed, which can restraint the behavior of particles in quantum space, and also can improve the search capability of the algorithm. Numerical simulations of the fractional-order Lorenz system and the fractional-order Chen system are conducted and the results demonstrate the effectiveness, robustness and versatility of the proposed algorithm.
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Keywords:
- fractional-order chaotic systems /
- parameter estimation /
- quantum parallel computation /
- quantum particle swarm optimization
[1] Sheikhan M, Shahnazi R, Garoucy S 2013 Neural Computing and Application 22 361
[2] Gandomi A H, Yun G J, Yang X S, Talatahari S 2013 Communications in Nonlinear Science and Numerical Simulation 18 327
[3] Yassi M, Yassi A, Yaghoobi M 2014 Iranian Conference on Intelligent Bam, Iran, February 4-6 2014 p1
[4] Gao X 2007 Ph. Dissertation D (Xian: Xidian University)) (in Chinese) [高心2005 博士学位论文(西安: 电子科技大学)]
[5] Ho W H, Chou J H, Guo C Y 2010 Nonlinear Dyn. 61 29
[6] Yang K Q, Maginu K J, Nomura H 2009 International Journal of Computer Mathematics 86 2225
[7] Chang, W D. 2007 Chaos Soliton. Fract. 32 1469
[8] Parlitz U, Junge L 1996 Phys. Rev. E 54 6253
[9] Wang L, Ye X, Ling P L 2011 Expert System with Applications 38 3238
[10] Long W, Jiao J J 2012 Acta Phys. Sin. 61 110507 (in Chinese) [龙文, 焦建军 2012 物理学报 61 110507]
[11] Lin J, Xu L 2013 Acta Phys. Sin. 62 030505 (in Chinese) [林剑, 许力 2013 物理学报 62 030505]
[12] Wang L, He W P, Wan S Q, Liao J L, He T 2014 Acta Phys. Sin. 63 019203 (in Chinese) [王柳, 何文平, 万仕全, 廖乐健, 何涛 2014 物理学报 63 019203]
[13] Wang D F, Zhang J Y, Wang X Y 2013 Chin. Phys. B 22 100504
[14] Li A P, Liu G R, Shen X Q 2013 Computer Engineering and Applications 49 4 (in Chinese) [李安平, 刘国荣, 沈细群 2013 计算机工程应用 49 4]
[15] Nielsen M, Chuang I 2010 Quantum Computation and Quantum Information (London: Cambridge University Press) pp 61-75
[16] Li S Y, Li P C 2007 Chinese Jounal of Quantum Electronics 24 569 (in Chinese) [李士勇, 李盼池 2007 量子电子学报 24 569]
[17] Caponetto R 2010 Fractional order systems: modeling and control applications (World Scientific) pp 62-65
[18] He Q, Wang L, Liu B 2007 Chaos Soliton. Fract. 34 645
[19] Li C, Chen G 2004 Chaos Soliton. Fract. 22 549
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[1] Sheikhan M, Shahnazi R, Garoucy S 2013 Neural Computing and Application 22 361
[2] Gandomi A H, Yun G J, Yang X S, Talatahari S 2013 Communications in Nonlinear Science and Numerical Simulation 18 327
[3] Yassi M, Yassi A, Yaghoobi M 2014 Iranian Conference on Intelligent Bam, Iran, February 4-6 2014 p1
[4] Gao X 2007 Ph. Dissertation D (Xian: Xidian University)) (in Chinese) [高心2005 博士学位论文(西安: 电子科技大学)]
[5] Ho W H, Chou J H, Guo C Y 2010 Nonlinear Dyn. 61 29
[6] Yang K Q, Maginu K J, Nomura H 2009 International Journal of Computer Mathematics 86 2225
[7] Chang, W D. 2007 Chaos Soliton. Fract. 32 1469
[8] Parlitz U, Junge L 1996 Phys. Rev. E 54 6253
[9] Wang L, Ye X, Ling P L 2011 Expert System with Applications 38 3238
[10] Long W, Jiao J J 2012 Acta Phys. Sin. 61 110507 (in Chinese) [龙文, 焦建军 2012 物理学报 61 110507]
[11] Lin J, Xu L 2013 Acta Phys. Sin. 62 030505 (in Chinese) [林剑, 许力 2013 物理学报 62 030505]
[12] Wang L, He W P, Wan S Q, Liao J L, He T 2014 Acta Phys. Sin. 63 019203 (in Chinese) [王柳, 何文平, 万仕全, 廖乐健, 何涛 2014 物理学报 63 019203]
[13] Wang D F, Zhang J Y, Wang X Y 2013 Chin. Phys. B 22 100504
[14] Li A P, Liu G R, Shen X Q 2013 Computer Engineering and Applications 49 4 (in Chinese) [李安平, 刘国荣, 沈细群 2013 计算机工程应用 49 4]
[15] Nielsen M, Chuang I 2010 Quantum Computation and Quantum Information (London: Cambridge University Press) pp 61-75
[16] Li S Y, Li P C 2007 Chinese Jounal of Quantum Electronics 24 569 (in Chinese) [李士勇, 李盼池 2007 量子电子学报 24 569]
[17] Caponetto R 2010 Fractional order systems: modeling and control applications (World Scientific) pp 62-65
[18] He Q, Wang L, Liu B 2007 Chaos Soliton. Fract. 34 645
[19] Li C, Chen G 2004 Chaos Soliton. Fract. 22 549
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